This paper selectively reviews the literature on behavioural finance, focusing on the aggregate market implications of the behavioural biases that this literature has identified. Advocates of behavioural economics and finance argue that economic agents behave in a way which departs significantly and systematically from the axioms of expected utility theory. The paper surveys the main “anomalies” identified by this literature in the light of their possible implications on aggregate market behaviour. In particular, the anomalies are categorised into (i) those derived from cognitive limitations (bounded rationality), (ii) those determined by the interference of agents’ emotional state, (iii) those determined by choice bracketing, and (iv) those which suggest that a pre-determined set of preferences does not exist altogether. Moreover, prospect theory is surveyed in particular detail, as it has become a serious challenger to expected utility in economics and finance due to the empirical support, its mathematical tractability and its being consistent with rational expectations. Finally, the paper claims that while convincing evidence against market rationality in the beatthe- market sense is yet to be provided, many indications are now available that financial markets may indeed be “irrational” in other reasonable and relevant meanings.